Mathematical Models of Mass Transfer in Tissue for Molecular Medicine Reversible Electroporation - Porous Media: Applications in Biological Systems and Biotechnology - page 48

The electroporation process is dicult to isolate from other processes that
occur in the cell and its membrane. Many parameters affect the triggering
and amplitude of electroporation, so under different conditions the behavior
of the cell may be dicult to analyze. An effort to model electroporation
as an isolated phenomenon would require strict calibration and control of
many environmental parameters during electroporation tests and measure-
ments. For example, when hydraulic stress is applied, the transmembrane
potential threshold is decreased so pores start to form under conditions that
would not cause normal cells to go through electroporation. Furthermore, elec-
troporation is not unique in the sense that similar phenomena due to other
causes can be observed, unrelated to transmembrane potential. This is true
for both creating pores in the membrane as well as sealing them. The ability of
the cell to reseal, for example, after a mechanical puncture of the membrane
has been studied carefully (Steinhardt et al. 1994; McNeil and Steinhardt
1997). Similar mechanisms may be involved in the resealing of the mem-
brane after electroporation. This makes the isolated study of this process quite
challenging.
In this chapter, we will review several aspects of the electroporation pro-
cess and how it is used to introduce drugs into cells in a specific part of a
tissue. We begin by describing the fundamental mechanism of electropora-
tion and continue with some mathematical models of ion transport during
the process. We then describe a method of monitoring and controlling in vivo
electroporation and relate that to mass transfer in tissue, which gives rise to
a hierarchical model for drug delivery using electroporation.

2.2 Fundamental Aspects of Reversible Electroporation
The electroporation process can be divided into five steps (Teissie et al. 2005):

1. Excitation

2. Pore expansion

3. Stabilization

4. Resealing

5. Long-term recovery

In the excitation stage, the membrane is excited by some high voltage pulse
and becomes more permeable due to the creation of pores, roughly the size
of 1 nm (Weaver and Chizmadzhev 1996). This is perhaps the most elusive
part of the electroporation process, and different theories exist on how exactly
these initial “aqueous pathways” are created. One of the leading assumptions
describes this initial stage as the creation of hydrophobic pores. A bilayer
lipid membrane at rest that may look like the schematic diagram shown in